报告题目 (Title)：Reduction of lattice equations: Lecture I（离散方程的约化）

报告人 (Speaker)： Peter van der Kamp 教授（La Trobe University, Australia）

报告时间 (Time)：2022年09月01日(周四) 09:00-10:00

报告地点 (Place)：Zoom会议 （ID：882 4175 6007）

邀请人(Inviter)：张大军

主办部门：理学院数学系

报告摘要：Lecture 1 Topics: Lattice equations, Consistency Around the Cube, Lax pairs, including for multi-component systems

Narrative: A lattice equation is a relation between points on a lattice called a stencil, the stencil can be translated over the lattice and the corresponding equations should hold everywhere on the lattice. Often the stencil is an elementary square (of the 2D lattice), also called a quad. Such equations are called Consistent Around the Cube (CAC) if they can be consistently defined on the face of a 3D cube. CAC quad equations can be defined on more general quad-graphs and higher dimensional lattices. For a lattice equation which is CAC, one can derive a Lax pair, which is a system of linear equations whose consistency is equivalent to the equation. This procedure also works for systems of lattice equations.